We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price [Formula: see text] is given by the supremum over the prices of the American option under randomized models. That is, [Formula: see text], where [Formula: see text] and the martingale measure [Formula: see text] are chosen such that [Formula: see text] and [Formula: see text] prices the European options correctly, and [Formula: see text] is the price of the American option under the model [Formula: see text]. Our result generalizes the example given in Hobson & Neuberger (2016) that the highest model-based price can be considered as a randomization over models.
Dynamic Trading Strategies and Portfolio Choice
